This article gives a review of our latest results on the self-pulsation and excitability properties of blue-violet lasers. A number of investigations of the phenomena in InGaN lasers with different designs are described. The bifurcations, which are the origin of the phenomena, are identified and the effects of the lasers parameters on device dynamics are discussed. It is shown how different laser structures can be used to control device behaviour and the dependence of self-pulsation and excitability behaviour on laser geometry is discussed. Finally, agreement between the results of numerical calculations and experimental measurements on self-pulsation is demonstrated.